1

SRI BINTANG TUITION CENTRE Additional Mathematics Form 4 (Thu)

Monthly Test – August 2009 1 hour

Name:………………………………

Important Formulae

1 2 4

2

b b acx

a

− ± −=

2 am × an = a

m + n

3 am ÷ an = a m - n

4 (am) n = a nm

5 loga mn = log am + loga n

6 loga n

m = log am - loga n

7 log a mn = n log a m

8 logab = a

b

c

c

log

log

9 Distance = 2

21

2

21 )()( yyxx −+−

10 Midpoint

(x , y) =

+

2

21 xx ,

+

2

21 yy

11 A point dividing a segment of a line

( x,y) = ,21

+

+

nm

mxnx

+

+

nm

myny 21

12 Area of triangle

= )()(2

1312312133221 1

yxyxyxyxyxyx ++−++

13 Arc length, s = rθ

14 Area of sector , L = 21

2r θ

Answer all questions. Show your working steps.

1. Given the functions xxf 32: −a and baxxg +2: a . If 56)( += xxfg , find the

value of a and of b.

[3 marks]

2. The quadratic equation 03)1(2 2=−−+ xpkx has roots two equal roots. Given that

pk6

1= , calculate the value of p.

[3 marks]

2

3. Solve the inequality 172)32( 2≥−− xx .

[3 marks]

4. Solve the simultaneous equations

03

02

22=+−

=+−

yyx

yx

[4 marks]

5. Solve the equation )2(43)2(212 xx

−=+ .

[3 marks]

3

6. Given that x=5log2 and that xy 32125 =+ . Find the value of y.

[4 marks]

7. (a) Given the distance between the point )8,1( R and ),10( pS is 15 units. Find the

value of p.

(b) Find the possible values of k if the area of the triangle with vertices

),4(),1,2( kTS − and )5,1( −V is 2

110 units

2.

[5 marks]

4

8.

The diagram shows a major sector OLNM with radius 8 cm and centre O. Given that o

OLM 20=∠ , find

(a) LOM∠ in radians,

(b) the major arc length LNM.

[5 marks]

N

O

L M

cm 8

o20

5

9. Solutions to this question by scale drawing will not be accepted.

Given that the equation of line YZ is 02443 =+− xy and the coordinates of point X

is (2, 3). Y lies on the x-axis and Z lies on the y-axis.

(a) Find

(i) the equation of the straight line XY,

(ii) the coordinates of Y and Z.

[4 marks]

(b) The straight line ZY is extended to a point A such that 4ZY = 3ZA. Find the

coordinates of A.

[3 marks]

(c) A point Q moves such that its distance from point X is always 6 units. Find the

equation of the locus of Q.

[3 marks]

y

xO

Z

Y

)3,2(X

02443 =+− xy